A Univariate Time Series Autoregressive Integrated Moving Average Model for the Exchange Rate Between Nigerian Naira and US Dollar

Nasiru Mukaila Olakorede; Samuel Olayemi Olanrewaju; Maji Yusufu Ugbede

doi:doi:10.11648/j.ajtas.20180705.12

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A Univariate Time Series Autoregressive Integrated Moving Average Model for the Exchange Rate Between Nigerian Naira and US Dollar

Nasiru Mukaila Olakorede, Samuel Olayemi Olanrewaju, Maji Yusufu Ugbede

Published in American Journal of Theoretical and Applied Statistics (Volume 7, Issue 5)

Received: 9 March 2018 Accepted: 30 March 2018 Published: 6 August 2018

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Abstract

This research fit a univariate time series ARIMA model to the Monthly data of exchange rate between Nigerian Naira and US Dollar from January 1980 to December 2015. The Box-Jenkins Autoregressive Integrated Moving Average (ARIMA) model was estimated and the best fitted ARIMA model is used to obtain the post-sample forecasts for three years (January 2016 to December 2018). The data was analyzed with the aid of R statistical package and the best model was selected using Auto. ARIMA. The fitted model is ARIMA (0,1,1) with Akaike Information Criteria (AIC) of 2313.19, Normalized Bayesian Information Criteria (BIC) of 2325.39. This model was further validated by Ljung-Box test with no significant Autocorrelation between the residuals at different lag times and subsequently by white noise of residuals from the diagnostic check performed which clearly portray randomness of the standard error of the residuals, no significant spike in the residual plots of ACF and PACF. The forecasts value indicates clearly that Naira will continue to depreciate against the US Dollar between the periodsunderstudy.

Published in	American Journal of Theoretical and Applied Statistics (Volume 7, Issue 5)
DOI	10.11648/j.ajtas.20180705.12
Page(s)	173-179
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2018. Published by Science Publishing Group

Keywords

Arima, Time Series, Box- Jenkins, Ljung-Box, Stationarity, Unit Root, Naira, US Dollar

References

[1]	Akpan, D. B. (2004). “Financial Liberalization and Endogenous Growth: The Case of Nigeria”. African Institute for Economic Development and Planning, Dakar
[2]	Appiah, S. T, and Adetunde, I. A(2011). Forecasting Exchange Rate between the Ghana Cedi’s and the US Dollars using Time Series Analysis. Current Research Journal of Economic Theory 3(2): 76-83co
[3]	Azeez, B. A., Kolapo, F. T and Ajayi, L. B. (2012).“Effect of Exchange rate Volatility on Macroeconomic Performance in Nigeria”
[4]	Babu A. S and Reddy S. K. (2015).“Exchange Rate Forecasting using ARIMA, Neural Network and Fuzzy Neuron”
[5]	Box, George E. P., Gwilym M. Jenkins(1976). “Time Series Analysis”. Revised Edition. Oakland, CA: Holden-Day
[6]	Fat Codruta Maria and Eva Dezsi (2011). “Exchange Rates Forecasting: Exponential Smoothing Techniques and ARIMA Models”. Annals of Faculty of Economics, Vol. 1, Issue 1, pp. 499-508
[7]	Jameela, O. Y. (2010). Exchange Rate Changes and Output Performance in Nigeria. A SectionalAnalysis
[8]	Maria, F. C., and Eva, D. (2011). Exchange rates forecasting: exponential smoothing techniques and ARIMAmodels. Anals of faculty of economics, 1, 499-508
[9]	Mordi, M. C. (2006). Challenges of Exchange Rate Volatility in Economic Management of Nigeria, Inthe Dynamic of Exchange Rate in Nigeria, CBN Bullion Vol. 30 (3), July September. Pp. 17-25
[10]	Onasanya, Olanrewaju, K. and Adeniyi, Oyebimpe, E. (2011). Forecasting of Exchange Rate Between Naira and US Dollar Using Time Domain Model. International Journal of Development and Economic sustainability. Vol. 1, No. 1, pp. 45-55
[11]	Salau M. O (1998). ARIMA modeling of Nigeria’s crude oil Export, AMSE, Modeling, Measurement and control. Vol. 18. No. 1, pp. 1-20
[12]	Vergil, H., & Özkan, F. (2007). Döviz Kurları Öngörüsünde Parasal Model ve ArimaModelleri: Türkiye Örneği. Retrieved from http://dergipark.gov.tr/kosbed/issue/25707/271265

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APA Style

Nasiru Mukaila Olakorede, Samuel Olayemi Olanrewaju, Maji Yusufu Ugbede. (2018). A Univariate Time Series Autoregressive Integrated Moving Average Model for the Exchange Rate Between Nigerian Naira and US Dollar. American Journal of Theoretical and Applied Statistics, 7(5), 173-179. https://doi.org/10.11648/j.ajtas.20180705.12

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ACS Style

Nasiru Mukaila Olakorede; Samuel Olayemi Olanrewaju; Maji Yusufu Ugbede. A Univariate Time Series Autoregressive Integrated Moving Average Model for the Exchange Rate Between Nigerian Naira and US Dollar. Am. J. Theor. Appl. Stat. 2018, 7(5), 173-179. doi: 10.11648/j.ajtas.20180705.12

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AMA Style

Nasiru Mukaila Olakorede, Samuel Olayemi Olanrewaju, Maji Yusufu Ugbede. A Univariate Time Series Autoregressive Integrated Moving Average Model for the Exchange Rate Between Nigerian Naira and US Dollar. Am J Theor Appl Stat. 2018;7(5):173-179. doi: 10.11648/j.ajtas.20180705.12

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@article{10.11648/j.ajtas.20180705.12,
  author = {Nasiru Mukaila Olakorede and Samuel Olayemi Olanrewaju and Maji Yusufu Ugbede},
  title = {A Univariate Time Series Autoregressive Integrated Moving Average Model for the Exchange Rate Between Nigerian Naira and US Dollar},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {7},
  number = {5},
  pages = {173-179},
  doi = {10.11648/j.ajtas.20180705.12},
  url = {https://doi.org/10.11648/j.ajtas.20180705.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20180705.12},
  abstract = {This research fit a univariate time series ARIMA model to the Monthly data of exchange rate between Nigerian Naira and US Dollar from January 1980 to December 2015. The Box-Jenkins Autoregressive Integrated Moving Average (ARIMA) model was estimated and the best fitted ARIMA model is used to obtain the post-sample forecasts for three years (January 2016 to December 2018). The data was analyzed with the aid of R statistical package and the best model was selected using Auto. ARIMA. The fitted model is ARIMA (0,1,1) with Akaike Information Criteria (AIC) of 2313.19, Normalized Bayesian Information Criteria (BIC) of 2325.39. This model was further validated by Ljung-Box test with no significant Autocorrelation between the residuals at different lag times and subsequently by white noise of residuals from the diagnostic check performed which clearly portray randomness of the standard error of the residuals, no significant spike in the residual plots of ACF and PACF. The forecasts value indicates clearly that Naira will continue to depreciate against the US Dollar between the periodsunderstudy.},
 year = {2018}
}

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TY  - JOUR
T1  - A Univariate Time Series Autoregressive Integrated Moving Average Model for the Exchange Rate Between Nigerian Naira and US Dollar
AU  - Nasiru Mukaila Olakorede
AU  - Samuel Olayemi Olanrewaju
AU  - Maji Yusufu Ugbede
Y1  - 2018/08/06
PY  - 2018
N1  - https://doi.org/10.11648/j.ajtas.20180705.12
DO  - 10.11648/j.ajtas.20180705.12
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
SP  - 173
EP  - 179
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20180705.12
AB  - This research fit a univariate time series ARIMA model to the Monthly data of exchange rate between Nigerian Naira and US Dollar from January 1980 to December 2015. The Box-Jenkins Autoregressive Integrated Moving Average (ARIMA) model was estimated and the best fitted ARIMA model is used to obtain the post-sample forecasts for three years (January 2016 to December 2018). The data was analyzed with the aid of R statistical package and the best model was selected using Auto. ARIMA. The fitted model is ARIMA (0,1,1) with Akaike Information Criteria (AIC) of 2313.19, Normalized Bayesian Information Criteria (BIC) of 2325.39. This model was further validated by Ljung-Box test with no significant Autocorrelation between the residuals at different lag times and subsequently by white noise of residuals from the diagnostic check performed which clearly portray randomness of the standard error of the residuals, no significant spike in the residual plots of ACF and PACF. The forecasts value indicates clearly that Naira will continue to depreciate against the US Dollar between the periodsunderstudy.
VL  - 7
IS  - 5
ER  -

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Author Information

Nasiru Mukaila Olakorede

Department of Statistics, University of Abuja, Abuja, Nigeria
Samuel Olayemi Olanrewaju

Department of Statistics, University of Abuja, Abuja, Nigeria
Maji Yusufu Ugbede

Department of Statistics, University of Abuja, Abuja, Nigeria

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APA Style

Nasiru Mukaila Olakorede, Samuel Olayemi Olanrewaju, Maji Yusufu Ugbede. (2018). A Univariate Time Series Autoregressive Integrated Moving Average Model for the Exchange Rate Between Nigerian Naira and US Dollar. American Journal of Theoretical and Applied Statistics, 7(5), 173-179. https://doi.org/10.11648/j.ajtas.20180705.12

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ACS Style

Nasiru Mukaila Olakorede; Samuel Olayemi Olanrewaju; Maji Yusufu Ugbede. A Univariate Time Series Autoregressive Integrated Moving Average Model for the Exchange Rate Between Nigerian Naira and US Dollar. Am. J. Theor. Appl. Stat. 2018, 7(5), 173-179. doi: 10.11648/j.ajtas.20180705.12

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AMA Style

Nasiru Mukaila Olakorede, Samuel Olayemi Olanrewaju, Maji Yusufu Ugbede. A Univariate Time Series Autoregressive Integrated Moving Average Model for the Exchange Rate Between Nigerian Naira and US Dollar. Am J Theor Appl Stat. 2018;7(5):173-179. doi: 10.11648/j.ajtas.20180705.12

Copy | Download

@article{10.11648/j.ajtas.20180705.12,
  author = {Nasiru Mukaila Olakorede and Samuel Olayemi Olanrewaju and Maji Yusufu Ugbede},
  title = {A Univariate Time Series Autoregressive Integrated Moving Average Model for the Exchange Rate Between Nigerian Naira and US Dollar},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {7},
  number = {5},
  pages = {173-179},
  doi = {10.11648/j.ajtas.20180705.12},
  url = {https://doi.org/10.11648/j.ajtas.20180705.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20180705.12},
  abstract = {This research fit a univariate time series ARIMA model to the Monthly data of exchange rate between Nigerian Naira and US Dollar from January 1980 to December 2015. The Box-Jenkins Autoregressive Integrated Moving Average (ARIMA) model was estimated and the best fitted ARIMA model is used to obtain the post-sample forecasts for three years (January 2016 to December 2018). The data was analyzed with the aid of R statistical package and the best model was selected using Auto. ARIMA. The fitted model is ARIMA (0,1,1) with Akaike Information Criteria (AIC) of 2313.19, Normalized Bayesian Information Criteria (BIC) of 2325.39. This model was further validated by Ljung-Box test with no significant Autocorrelation between the residuals at different lag times and subsequently by white noise of residuals from the diagnostic check performed which clearly portray randomness of the standard error of the residuals, no significant spike in the residual plots of ACF and PACF. The forecasts value indicates clearly that Naira will continue to depreciate against the US Dollar between the periodsunderstudy.},
 year = {2018}
}

Copy | Download

TY  - JOUR
T1  - A Univariate Time Series Autoregressive Integrated Moving Average Model for the Exchange Rate Between Nigerian Naira and US Dollar
AU  - Nasiru Mukaila Olakorede
AU  - Samuel Olayemi Olanrewaju
AU  - Maji Yusufu Ugbede
Y1  - 2018/08/06
PY  - 2018
N1  - https://doi.org/10.11648/j.ajtas.20180705.12
DO  - 10.11648/j.ajtas.20180705.12
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
SP  - 173
EP  - 179
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20180705.12
AB  - This research fit a univariate time series ARIMA model to the Monthly data of exchange rate between Nigerian Naira and US Dollar from January 1980 to December 2015. The Box-Jenkins Autoregressive Integrated Moving Average (ARIMA) model was estimated and the best fitted ARIMA model is used to obtain the post-sample forecasts for three years (January 2016 to December 2018). The data was analyzed with the aid of R statistical package and the best model was selected using Auto. ARIMA. The fitted model is ARIMA (0,1,1) with Akaike Information Criteria (AIC) of 2313.19, Normalized Bayesian Information Criteria (BIC) of 2325.39. This model was further validated by Ljung-Box test with no significant Autocorrelation between the residuals at different lag times and subsequently by white noise of residuals from the diagnostic check performed which clearly portray randomness of the standard error of the residuals, no significant spike in the residual plots of ACF and PACF. The forecasts value indicates clearly that Naira will continue to depreciate against the US Dollar between the periodsunderstudy.
VL  - 7
IS  - 5
ER  -

Copy | Download